Finite Group Databasebeta

← C2×#21436753 #29468270

Subgroups — C2×#21436753 #29468270

Order 15104.

1970 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838134C211yesmaximal, characteristic, complemented
2C2×#16838108C211yesmaximal, characteristic, complemented
3#21436753C2116yesmaximal, direct product factor
4C2×#16837758C211yesmaximal, characteristic, complemented
5C2×#16837747C211yesmaximal, characteristic, complemented
6C2×#16837695C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837699C211yesmaximal, characteristic, complemented
9C2×#16837620C211yesmaximal, characteristic, complemented
10C2×#16837614C211yesmaximal, characteristic, complemented
11C2×#16837596C211yesmaximal, characteristic
12C2×C8×Dic118C211yesmaximal, characteristic, complemented
13C2×#16837487C211yesmaximal, characteristic, complemented
14C2×C4×D472C211yesmaximal, characteristic, complemented
15C2×#16837482C211yesmaximal, characteristic, complemented
16C2×C59×#488C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×D472C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20#16838134—24no—
21#16838134C2218yescomplemented
22#16838108—24no—
23#16838108C2218yescomplemented
24C2×#14273726C2211yescharacteristic
25C2×#14273723C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273716C2211yescharacteristic
28C2×#14273713—21no—
29C2×#14273711—21no—
30C2×#14273709—21no—
31C2×#14273707—21no—
32C2×#14273705—21no—
33C2×#14273705—21no—
34C2×Q8×Dic59C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×C4×D236C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×(C22⋊D59)⋊C4—21no—
42C2×C4⋊C4×D59—21no—
43#16837758C2218yescomplemented
44#16837747C2218yescomplemented
45#16837700C2218yescomplemented
46#16837699C2218yescomplemented
47#16837695C2218yescomplemented
48#16837620C2218yescomplemented
49#16837614C2218yescomplemented
50#16837596C2218yes—
51C8×Dic118C2218yescomplemented
52#16837487C2218yescomplemented
53C4×D472C2218yescomplemented
54#16837482C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C59×#488C2218yescomplemented
72C2×#103×C59C2211yescharacteristic
73C2×#103×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C23×Dic59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C2×#11745671—24no—
89C2×#11745671C2314yes—
90C2×D472—24no—
91C2×D472C2314yes—
92C2×#11745669—24no—
93C2×#11745669C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273726—22no—
97#14273726C2314yes—
98#14273723—22no—
99#14273723C2314yes—
100#14273718—22no—
101#14273718C2314yes—
102#14273716—22no—
103#14273716C2314yes—
104#14273713—28no—
105#14273711—28no—
106#14273709—28no—
107#14273707—28no—
108#14273705—28no—
109#14273705—28no—
110Q8×Dic59—22no—
111Q8×Dic59C2314yes—
112C4×Dic118D414yes—
113C4×Dic118C2314yes—
114C4×D236—22no—
115C4×D236—22no—
116C4×D236C2314yes—
117C4×D236C2314yes—
118D4×Dic59—22no—
119D4×Dic59C2314yes—
120#14273689—22no—
121#14273689—22no—
122#14273689C2314yes—
123#14273689C2314yes—
124(C22⋊D59)⋊C4—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59D411yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C4⋊C4×D59—28no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59C2311yescharacteristic
144C2×C4×Dic59C2311yescharacteristic
145#14273661C2314yes—
146#14273660C2314yes—
147#14273658C2314yes—
148C4⋊(C59⋊C8)C2314yes—
149Dic59⋊C8C2314yes—
150Dic59⋊C8C2314yes—
151#14273651C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273648C2314yes—
155#14273647C2314yes—
156#14273647C2314yes—
157C8×Dic59C2314yes—
158C8×Dic59C2314yes—
159C22×Q8×C59C2311yescharacteristic
160C22×D4×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163#125×C59—22no—
164#125×C59C2314yes—
165#124×C59—22no—
166#124×C59C2314yes—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C22⋊C4×C59—21no—
172C2×C22⋊C4×C59—21no—
173C2×C42×C59C2311yescharacteristic
174#103×C59C2314yes—
175#103×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C4×C8×C59C2314yes—
179C24×C59—21no—
180C23×D59—21no—
181C23×D59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59C2412yes—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59—22no—
189C2×D4×C59C2412yes—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—82no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—24no—
203C22×Dic59—82no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C2×D236—21no—
209C2×D236—22no—
210C2×D236—22no—
211C2×D236—22no—
212C2×D236—21no—
213C2×D236#4114yes—
214C2×D236C2412yes—
215C2×D236C2412yes—
216C2×C4×D59—24no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—24no—
220C2×C4×D59—44no—
221C2×C4×D59—82no—
222C2×C4×D59—82no—
223C2×C4×D59—82no—
224C2×Dic118—24no—
225C2×Dic118—24no—
226C2×Dic118—82no—
227C2×Dic118C2×D414yes—
228C2×C8×C59—22no—
229C2×C8×C59—22no—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C22⋊Dic59—24no—
243#11745671—28no—
244#11745669—28no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2×D414yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4C2×D414yes—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59C2×D412yes—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C4×Dic59C2412yes—
267C2×C59⋊C8—22no—
268C2×C59⋊C8—22no—
269C2×C59⋊C8C2412yes—
270C2×C59⋊C8C2412yes—
271D472—28no—
272C23×C59—22no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59C22×D411yescharacteristic
277C22×D59—24no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—42no—
281C22×D59—42no—
282C22×D59—42no—
283C22×D59—42no—
284C22×D59—42no—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—42no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—42no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C2×#4112yes—
303C2×C4×C592−1+412yes—
304C2×C4×C59C2511yescharacteristic
305C22⋊D59—48no—
306C22⋊D59—84no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—42no—
313C2×Dic59—42no—
314C2×Dic59—84no—
315C2×Dic59#13514yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320D236—24no—
321D236—22no—
322D236—22no—
323D236—22no—
324D236—42no—
325D236C2×#4114yes—
326C4×D59—48no—
327C4×D59—84no—
328C4×D59—84no—
329C4×D59—84no—
330Dic118—28no—
331Dic118—84no—
332C8×C59—22no—
333C8×C59—22no—
334C59⋊C8—22no—
335C59⋊C8—22no—
336C2×#3361—591nomaximal, Sylow
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—84no—
341C22×C59#54812yes—
342C22×C59C2×#13512yes—
343C22×C59#57612yes—
344C22×C59C23×D411yescharacteristic
345C2×D59—24no—
346C2×D59—48no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—84no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59#54812yes—
359C4×C59C22×#4111yescharacteristic
360C4×C59C2×2−1+411yescharacteristic
361Dic59—22no—
362Dic59—22no—
363Dic59—22no—
364Dic59—42no—
365Dic59—42no—
366Dic59C2×#13514yes—
367C2×#559—591no—
368C2×#554—591no—
369#3361—5916no—
370C2×#488—591no—
371C2×#488D5911yescharacteristic, complemented
372C2×#486—591no—
373C2×#477—591no—
374C2×#478—591no—
375C2×#478—591no—
376C2×#463—591no—
377C2×#463—591no—
378C2×#459—591no—
379C2×C8×Q8—591no—
380C2×C4×SD16—591no—
381C2×C4×D8—591no—
382C2×C4×D8—591no—
383C2×C59—82no—
384C2×C59#336114yescomplemented
385C2×C59C2×#54811yescharacteristic
386C2×C59C22×#13511yescharacteristic
387C2×C59C2×#57611yescharacteristic
388D59—44no—
389D59—82no—
390C22×SD16—591no—
391C22×D8—591no—
392C22×D8—591no—
393#559—598no—
394#559—1184no—
395#554—598no—
396#554—1184no—
397C2×C4⋊Q8—591no—
398C2×#127—591no—
399C2×#125—591no—
400C2×#125C2×D5911yescharacteristic
401C2×#124—591no—
402C2×#124—1181no—
403C2×#124C2×D5911yescharacteristic
404C2×#123—1181no—
405C2×#123—1181no—
406C2×C22⋊Q8—1181no—
407C2×C22⋊Q8—1181no—
408C2×C22⋊Q8—1181no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×D4—591no—
412C2×C4×D4—591no—
413C2×C4×D4—591no—
414C2×C4×D4—591no—
415C2×C4×D4—591no—
416C2×C4×D4—1181no—
417C22×C4⋊C4—1181no—
418#488—598no—
419#488C2×D5918yescomplemented
420#486—598no—
421#478—598no—
422#478—598no—
423#477—598no—
424#463—598no—
425#463—598no—
426#459—598no—
427C8×Q8—598no—
428C4×SD16—598no—
429C4×D8—598no—
430C4×D8—598no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#106—591no—
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×C4⋊C8—591no—
437C2×#103—591no—
438C2×#103C2×D5911yescharacteristic
439C2×#103C2×D5911yescharacteristic
440C2×#102—591no—
441C2×#102—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×#102—591no—
445C2×#102C2×D5911yescharacteristic
446C2×#102C2×D5911yescharacteristic
447C2×C4×C8—591no—
448C2×C4×C8—591no—
449C2×C4×C8C2×D5911yescharacteristic
450C59C2×#336111yescharacteristic, complemented, Sylow
451C22×Q8—591no—
452C22×Q8—1181no—
453C22×Q8C22×D5911yescharacteristic
454C22×D4—591no—
455C22×D4—591no—
456C22×D4—1181no—
457C22×D4—1181no—
458C22×D4C22×D5911yescharacteristic
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4—1181no—
463C23×C4—1181no—
464C2×SD16—594no—
465C2×SD16—1184no—
466C2×D8—594no—
467C2×D8—594no—
468C2×D8—1184no—
469C2×D8—1184no—
470C22×C8—591no—
471C22×C8—591no—
472C22×C8C22×D5911yescharacteristic
473C22×C8C22×D5911yescharacteristic
474C4⋊Q8—594no—
475C4⋊Q8—1182no—
476#127—594no—
477#127—1182no—
478#125—22no—
479#125—594no—
480#125—1182no—
481#125C22×D5914yes—
482#124—22no—
483#124—594no—
484#124—1182no—
485#124—1188no—
486#124C22×D5914yes—
487#123—1188no—
488#123—1188no—
489C22⋊Q8—1188no—
490C22⋊Q8—1188no—
491C22⋊Q8—1188no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×D4—594no—
497C4×D4—594no—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—1182no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4—1182no—
506C4×D4—1182no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—1188no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42C22×D5911yescharacteristic
534#107—594no—
535#107—594no—
536#106—594no—
537C4⋊C8—594no—
538C4⋊C8—594no—
539C4⋊C8—594no—
540#103—594no—
541#103C22×D5914yes—
542#103C22×D5914yes—
543#102—594no—
544#102—594no—
545#102—594no—
546#102—594no—
547#102—594no—
548#102C22×D5914yes—
549#102C22×D5914yes—
550C4×C8—594no—
551C4×C8—594no—
552C4×C8C22×D5914yes—
553C24—21no—
554C24—1181no—
555C24—1181no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—594no—
560C2×Q8—1184no—
561C2×Q8—1184no—
562C2×Q8—4722no—
563C2×Q8C23×D5912yes—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—594no—
568C2×D4—592no—
569C2×D4—592no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1181no—
573C2×D4—1181no—
574C2×D4—1182no—
575C2×D4—1182no—
576C2×D4—1182no—
577C2×D4—4722no—
578C2×D4—2364no—
579C2×D4C23×D5912yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—591no—
584C22×C4—591no—
585C22×C4—591no—
586C22×C4—591no—
587C22×C4—1184no—
588C22×C4—1184no—
589C22×C4—1184no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1184no—
593C22×C4—1184no—
594C22×C4—4722no—
595C22×C4—4722no—
596C22×C4—4722no—
597C22×C4—4722no—
598C22×C4—2364no—
599C22×C4D4×D5911yescharacteristic
600C22×C4D4×D5911yescharacteristic
601C22×C4C23×D5911yescharacteristic
602SD16—1188no—
603D8—1188no—
604D8—1188no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—592no—
608C2×C8—592no—
609C2×C8—1182no—
610C2×C8—1182no—
611C2×C8C23×D5912yes—
612C2×C8C23×D5912yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—594no—
618C4⋊C4—594no—
619C4⋊C4—594no—
620C4⋊C4—592no—
621C4⋊C4—592no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1181no—
627C4⋊C4—1181no—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—592no—
640C42—592no—
641C42—592no—
642C42—592no—
643C42—1184no—
644C42D4×D5912yes—
645C42C23×D5912yes—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—1182no—
651C23—1184no—
652C23—1182no—
653C23—2362no—
654C23—2362no—
655C23—2362no—
656C23—2362no—
657C23—2362no—
658C23C2×D4×D5911yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—1188no—
663Q8—4724no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—594no—
668D4—1182no—
669D4—1182no—
670D4—1182no—
671D4—1184no—
672D4—4724no—
673D4—2368no—
674D4—2362no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—594no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—592no—
687C2×C4—592no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—4724no—
694C2×C4—4724no—
695C2×C4—4724no—
696C2×C4—4724no—
697C2×C4—2368no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4C2×D4×D5912yes—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#1427377412yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—1184no—
715C22—4724no—
716C22—2362no—
717C22—2362no—
718C22—2362no—
719C22—2368no—
720C22—2362no—
721C22—2362no—
722C22#1683806012yes—
723C22#135×D5912yes—
724C22#1683820412yes—
725C22C22×D4×D5911yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—594no—
732C4—1182no—
733C4—1182no—
734C4—1182no—
735C4—2362no—
736C4—2362no—
737C4#1683806012yes—
738C4C2×#41×D5911yescharacteristic
739C4C2×#1427377411yescharacteristic
740C2—82no—
741C2—4722no—
742C2—2364no—
743C2#2143675314yesdirect product factor
744C2C2×#1683806011yescharacteristic
745C2C2×#135×D5911yescharacteristic
746C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#488C2
socleC23×C59C22×D4
prime radicalC2×#16837596C2
hypercenterC2×#488D59
hypocenterC59C2×#3361
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16838134C2semidirect
2. C2×#16838108C2semidirect
3. #21436753C2direct (N × H)
4. C2×#16837758C2semidirect
5. C2×#16837747C2semidirect
6. C2×#16837695C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837699C2semidirect
9. C2×#16837620C2semidirect
10. C2×#16837614C2semidirect
12. C2×C8×Dic118C2semidirect
13. C2×#16837487C2semidirect
14. C2×C4×D472C2semidirect
15. C2×#16837482C2semidirect
16. C2×C59×#488C2semidirect
21. #16838134C22semidirect
23. #16838108C22semidirect
43. #16837758C22semidirect
44. #16837747C22semidirect
45. #16837700C22semidirect
46. #16837699C22semidirect
47. #16837695C22semidirect
48. #16837620C22semidirect
49. #16837614C22semidirect
51. C8×Dic118C22semidirect
52. #16837487C22semidirect
53. C4×D472C22semidirect
54. #16837482C22semidirect
71. C59×#488C22semidirect
371. C2×#488D59semidirect
384. C2×C59#3361semidirect
419. #488C2×D59semidirect
450. C59C2×#3361semidirect
743. C2#21436753direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168381342
C2×#168381082
#214367532
C2×#168377582
C2×#168377472
C2×#168376952
C2×#168377002
C2×#168376992
C2×#168376202
C2×#168376142
C2×#168375962
C2×C8×Dic1182
C2×#168374872
C2×C4×D4722
C2×#168374822
C2×C59×#4882
C2×#336159